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Apr 3, 2024
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Name e, 174 Planetary Orbit Simulator — Student Guide V\yan (/7(0;\/1 Background Material Answer the following questions afier reviewing the “Kepler's Laws and Planctary Motion” and “Newton and Planetary Motion” background pages. Question 1: Draw a line connecting each law on the left with a description of it on the right. Kepler’s 2™ Law only a force acting on an object can change its motio planets move faster when close to the sun planets orbit the sun in elliptical paths planets with large orbits take a ong time to complete an orbi Question 2: When written as P> = a’ Kepler's 3rd Law (with P in years and a in AU) is applicable to ... a) any object orbiting our sun. b) any object orbiting any star. ) any object orbiting any other object. Question 3: The ellipse to the right has an eccentricity of about ... a) 0.25 b) 0.5 © 075 d) 0.9 Question 4: For a planet in an elliptical orbit to “sweep out equal areas in equal amounts of time” it must . a) move slowest when near the sun (® move fastest when near the sun c) move at the same speed at all times d) have a perfectly circular orbit NAAP — Planetary Orbit Simulator 1/8
Oueation 5 1170 planet i iwice a8 fatr (Yoo the oo of aphe m than at perih . then 1h wtrenpth of the gravitational force sl aphelion will be a) four times as much b)) twice as much ¢) the same d) one half as much @ one quarter as much Kepler's 1st Law If you have not already done so, launch the NAAP Planetary Orbit Simulator « Open the Kepler’s 1% Law tab if it is not already (it's [ rjp: You can change open by default). the value of a slider f A by clicking on the « Enable all 5 check boxes. slider bar or by entering a number n e The white dot is the “simulated planet”. One can click on the value box. it and drag it around. « Change the size of the orbit with the semimajor axis slider. Note how the background grid indicates change in scale while the displayed orbit size remains the same. « Change the eccentricity and note how it affects the shape of the orbit. Be aware that the ranges of several parameters are limited by practical issues that occur when creating a simulator rather than any true physical limitations. We have limited the semi-major axis to 50 AU since that covers most of the objects in which we are interested in our solar system and have limited eccentricity to 0.7 since the ellipses would be hard to fit on the screen for larger values. Note that the semi-major axis is aligned horizontally for all elliptical orbits created in this simulator, where they are randomly aligned in our solar system. « Animate the simulated planet. You may need to increase the animation rate for very large orbits or decrease it for small ones. « The planetary presets set the simulated planet’s parameters to those like our solar system’s planets. Explore these options. Question 6: For what eccentricity is the secondary focus (which is usually empty) located at the sun? What is the shape of this orbit? OQC, Tltl\s mq)(p 9 Fg,( {'ZLT (}rc/e Question 7: Create an orbit with a =20 AU and e = 0. Drag the planet first to the far left of the ellipse and then to the far right. What are the values of r; and r; at these locations? NAAP — Planetary Orbit Simulator 2/8
\ [ mmn’ r2 (AU) %"%"W,,2O | 2O Far Right 20 i ;_2 Og, — Question 8: Create an orbit with a = 20 AU and ¢ = 0.5. Drag the planet first to the far left of the ellipse and then to the far right. What are the values of r; and rp at these locations? r (AU) r2(AU) RTINS 00§11 NS ) Vlrfur Right 30 ‘ 0 Question 9; For the ellipse with a =20 AU and e = 0.5, can you find a point in the orbit where 1, and r; are equal? Sketch the ellipse, the location of this point, and r; and ry in the space below. value of the sum of r; and r, and how does it relate to the ellipse - i - . A Iues:! 1S thas true for pses”? . [ OF all CLIPSC 13 Ty, U € AaV1 )< L YK
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L Question 11: It is easy to create an ellipse using a N loop of string and two thumbtacks, The string is . i )7 i g first stretched over the thumbtacks which act as /_—__7‘ oy foci. The string is then pulled tight using the pencil which can then trace out the ellipse. Assume that you wish to draw an ellipsc '// | with a semi-major axis of a = 20 cm and e = 0.5. Using what you have learned earlier in this lab, what would be the appropriate distances for a) the separation of the thumbtacks and b) the length of the alring,? Please fully explain how you determine these values @) _The semipajor axis is also the distance between the fwa foci,hecefure my ‘ 1 be 20cm between fhe thamb 4 /e the \/fiILLMV‘I e Mem veTween the Thumb Tack s / ; \ /. b) Thg STIinq 9065 befwegn T}\a 'chh rMJ T}Le Sem| minor ax(s p()mT To ca|(v 'flfB e Twill us&a Tf'avlqlr fofind fhe eW,fi‘ STring length =20+22, 36£22.%= b4 72’Ac/r; *J Kepler's 2nd Law ‘&’xf_\/ Q e Use the “clear optional features” button to remove the 1st Law features. ¢ Open the Kepler's 2nd Law tab. e Press the “start sweeping” button. Adjust the semimajor axis and animation rate so that the planet moves at a reasonable speed. ¢ Adjust the size of the sweep using the “adjust size” slider. e Click and drag the sweep segment around. Note how the shape of the sweep segment changes, but the area does not. ¢ Add more sweeps. Erase all sweeps with the “crase sweeps” button. e The “sweep continuously” check box will cause sweeps to be created continuously when sweeping. Test this option. Question 12: Erase all sweeps and create an ellipse with a =1 AU and e = 0. Set the fractional sweep size to one-twelfth of the period. Drag the sweep segment around. Does its size or shape change? J-l does I\O‘r }7&6(\\45@ W 159 pk),l’J‘:f,LT e LQ NAAP — Planetary Orbit Simulator 4/8
@ Mine 1 Question 13: Leave the semi Mmsion avie & a I AUJ and chanee the & nirieit 0.5, Drag the swee p segment atound and note that its size and shape change. Where the sweep segment the “skinniest™ Where is it the “fattest™ Where is the planet when it 15 sweeping oul each of these sepments? (What names do astronomers use for these positions?) I_‘ [5 5 Kinpie 1 of 1he l/ A tutheST PP P fr0w The ‘ 44 P . Suh ‘!H(J“ 1vl 'l\,f af periapsis O CloesT po Wil frev ¢ AN i | / Question 14: What cccentricity in the simulator gives the greatest variation of sweep segment shape? O. 7 Bhudie.s Question 15: Halley’s comet has a semimajor axis of about 18.5 AU, a period of 76 years, and an eccentricity of about 0.97 (so Halley’s orbit cannot be shown in this simulator.) The orbit of Halley’s Comet, the Earth’s Orbit, and the Sun are shown in the 4nd diagram below (not exactly to scale). Based upon what you know about Kepler’s 2 Law, explain why we can only see the comet for about 6 months every orbit (76 years)? When close Fo the sun the comet moves faster and Then slpws Jown JmsTim/fit dtfer )em@ the, ocbit of earcth NAAP — Planetary Orbit Simulator 5/8
Kepler's 3" |Law & Llap the “clenr options] fegtores ¢ Dpen the Kepler's 3rd Law tab v the (able Balo Question 16: Use the gimulator 1o complete the table below Object | P (years) n (AL) e L P l a icd jL_' 7"‘_1‘-w T ””“"7 EN B 1,00 4] ( / ] I’ }l J} l - ‘M.’n'k A 1.52 [ (’? l ')“ l (Jt . .39 2L | Ceres \#,(w] 2.77 0.08 Zf./() s ,;_ > }I('hmm 50.7 ] )‘,‘\(m 0.38 }rl/( L'r} 25/ ” et 7 Question 17: As the size of a planet’s orbit increases, what happens to its period? ,,'t,’. TS PO & e o e e eAs 4 / Question 18: Start with the Earth’s orbit and change the cccentricity to 0.6. Does > e F < changing the ccccnlricilfr change the period of/Tc planet? L T has no (fl'{e (j 45 v the orbit otill has the same Jistance Newtonian Features * Important: Use the “clear optional features” button to remove other features. * Open the Newtonian features tab. * Click both show vector boxes to show both the velocity and the acceleration c_)f the planet. Observe the direction and length of the arrows. The length is proportional to the values of the vector in the plot. Question 19: The acceleration vector is always pointing towards what object in the simulator? Tb‘q, Sun Question 20: Create an ellipse witha =5 AU and e = 0.5. For each marked location on the plot below indicate a) whether the velocity is increasing or decreasing at the point in NAAP — Planetary Orbit Simulator 6/8
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” the orbit (by circling the appropriate arrow) and b) the angle 0 between the velocity and acceleration vectors. Note that one is completed for you. QI ) W1 o-7 D)4 Jo405] T@ 0= 1) Question 21: Where do the maximum and minimum values of velocity occur in the orbit? ,’#,flp>.> (minimam) Feciapsls (maximin) Question 22: Can you describe a general rule which identifies where in the orbit velocity is increasing and where it is decreasing? What is the angle between the velocity and 0 a,];PSu ) ( o U el the velocity decreases. When leayving apgdpsis avd 91 1 poliapss | 7 Y 27 : ?fl_ixflmfi;fl;’biflg Ll OGN T e acceleration vectors at these times? YV hen 'Cq ving 'p"(, ap$ d)’J | 0° Jezmw;m Angle>90° L NAAP — Planetary Orbit Simulator 7/8